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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Species differences (size, development, location) and environmental changes impact population persistence and coexistence.
  • Understanding these dynamics is crucial for predicting ecosystem stability.

Purpose of the Study:

  • To develop a general theory for the coexistence of structured, interacting species in stochastic environments.
  • To provide a mathematical framework for analyzing species persistence under environmental fluctuations.

Main Methods:

  • Developed a theory for nonlinear, multi-species matrix models with stochastic parameters.
  • Utilized dominant Lyapunov exponents of random matrix products to determine long-term growth rates.
  • Established a coexistence criterion based on a convex combination of long-term growth rates at low densities.

Main Results:

  • The proposed coexistence criterion ensures stochastic persistence, where species density rarely drops to critically low levels.
  • Applications revealed that temporal autocorrelation can disrupt predator-prey coexistence.
  • Fluctuations in log-fecundity can enhance persistence in structured populations.

Conclusions:

  • The theory provides a robust framework for understanding species coexistence in dynamic ecosystems.
  • Environmental stochasticity has complex effects, potentially hindering or promoting coexistence depending on the specific ecological context.
  • Spatial and temporal heterogeneity favors the coexistence of long-lived, sedentary competitors.